Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-1+e^(2*x))/(3*x)
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Limit of (-1+3*x)/(5+x^2+7*x)
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Limit of 1+13*x/5
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Limit of (7+x+x^2)/(-1+e^x)
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Identical expressions
- one + thirteen *x/ five
- 1 plus 13 multiply by x divide by 5
- one plus thirteen multiply by x divide by five
- 1+13x/5
- 1+13*x divide by 5
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Similar expressions
- 1-13*x/5
Limit of the function 1+13*x/5
The solution
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/ 13*x\ lim |1 + ----| x->oo\ 5 /
$$\lim_{x \to \infty}\left(\frac{13 x}{5} + 1\right)$$
Limit(1 + (13*x)/5, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(\frac{13 x}{5} + 1\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{13 x}{5} + 1\right)$$ =
$$\lim_{x \to \infty}\left(\frac{\frac{13}{5} + \frac{1}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{\frac{13}{5} + \frac{1}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{u + \frac{13}{5}}{u}\right)$$
=
$$\frac{13}{0 \cdot 5} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{13 x}{5} + 1\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{13 x}{5} + 1\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(\frac{13 x}{5} + 1\right)$$ =
$$\lim_{x \to \infty}\left(\frac{\frac{13}{5} + \frac{1}{x}}{\frac{1}{x}}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{\frac{13}{5} + \frac{1}{x}}{\frac{1}{x}}\right) = \lim_{u \to 0^+}\left(\frac{u + \frac{13}{5}}{u}\right)$$
=
$$\frac{13}{0 \cdot 5} = \infty$$
The final answer:
$$\lim_{x \to \infty}\left(\frac{13 x}{5} + 1\right) = \infty$$
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\frac{13 x}{5} + 1\right) = \infty$$
$$\lim_{x \to 0^-}\left(\frac{13 x}{5} + 1\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{13 x}{5} + 1\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{13 x}{5} + 1\right) = \frac{18}{5}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{13 x}{5} + 1\right) = \frac{18}{5}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{13 x}{5} + 1\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{13 x}{5} + 1\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{13 x}{5} + 1\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{13 x}{5} + 1\right) = \frac{18}{5}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{13 x}{5} + 1\right) = \frac{18}{5}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{13 x}{5} + 1\right) = -\infty$$
More at x→-oo
The graph